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Assessing Mortality Deceleration
Marie Böhnstedt, Jutta Gampe; in Zusammenarbeit mit Nadine Ouellette (University of Montreal, Kanada), Gerda Claeskens (University of Leuven, Belgien), Hein Putter (Leiden University, Medical Center, Niederlande)
The deceleration of death rates at high ages due to selection in heterogeneous cohorts is a given fact. Because the frail tend to die first, death rates at high ages refer to the most robust individuals of a cohort. This leads to decelerating population mortality, i.e., the increase in mortality with age slows down at high ages. While this result is theoretically obvious, mortality deceleration can be difficult to assess statistically because the phenomenon relates to the tail of the lifespan distribution, for which data are by definition scarcer than at earlier ages. This may lead to diagnostics that favor models without apparent mortality deceleration; hence, mortality deceleration has repeatedly been contested empirically.
Standard techniques for model choice, such as Akaike’s Information Criterion (AIC), are based on criteria that are optimal in an average sense, which implies that areas of sparser data enter with lower weights. Putting a specific feature of a model “in focus” leads to modifications of these criteria, so that features in the tail area of the distribution receive a higher impact in the criterion. In this project, such Focused Information Criteria (FIC) for mortality deceleration are developed theoretically, and their properties are investigated in empirical studies.
The hypothesis that death rates decelerate at high ages as an effect of selection in heterogeneous cohorts is formalized in the gamma-Gompertz model, which therefore provides a suitable framework for assessing mortality deceleration. Yet, in this model framework the standard assumptions that underlie the usual statistical (likelihood-based) methods are violated due to a boundary parameter. This project derives the properties of estimators and testing procedures under such non-standard conditions and shows how model selection based on AIC has to be modified. In addition, a new version of the FIC, adapted to the non-standard conditions, is proposed as a powerful tool for detecting mortality deceleration.
Besides this, the project investigates how the performance of statistical techniques for assessing mortality deceleration is affected by issues of study design, such as sample size and the age range covered by a dataset. Especially at the oldest ages, scientific validation of the ages at death might be required to obtain reliable estimates of death rates. Validated datasets might thus include only individuals who survived beyond a certain age. Such limited data availability will impact the assessment of mortality deceleration. Based on the statistical concept of the Fisher information, the project will quantify the effects of sample size or restricted age ranges on, for example, the power of the likelihood ratio test to detect mortality deceleration.
Alterung, Sterblichkeit und Langlebigkeit, Statistik und Mathematik
Lifetime Data Analysis 27:3, 333–356. (2021)
Statistics and Probability Letters 150, 68–73. (2019)
arXiv e-prints 1905.05760. unpublished. (2019)